Picard Approximation of Fixed Points of Nonexpansive Mappings

摘要

Let C be a bounded convex subset in a uniformly convex Banach space X, x_0, u_n implied by C, then x_(n+1) = S_nx_n, where S_n = alpha _(n0) I + alpha _(n1) T + alpha _(n2) T~2 + … + alpha _(nk) T~k + gamma _n u_n, alpha _(ni) >= 0, 0 < alpha <= alpha _(n0) <= b < 1, sum from i = 0 to k of (alpha _(ni)) + gamma _n = 1, and n >= 1. It is proved that x_n converges to a fixed point on T if T is a nonexpansive mapping.